Carmen has $30 in store bucks and a 25% discount coupon for a local department store. what maximum dollar amount can carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax? (note: the $30 store bucks are applied before the 25% discount is applied.)

$110

Step-by-step explanation:

Let x represent the amount of the purchase.  Since the $30 in store credit is applied before the 25% discount, we first subtract 30 from the price:

x-30

Taking a 25% discount means that Carmen pays 100-25 = 75% of the price.  75% = 75/100 = 0.75; this gives us

0.75(x-30)

Since it can be no more than 60, we use the inequality "less than or equal to"; this gives us

0.75(x-30) ≤ 60

Using the distributive property,

0.75(x)-0.75(30) ≤ 60

0.75x - 22.5 ≤ 0

Add 22.5 to each side:6

0.75x - 22.5 + 22.5 ≤ 60+22.5

0.75x ≤ 82.5

Divide each side by 0.75:

0.75x/0.75 ≤ 82.5/0.75

x ≤ 110

The largest purchase price she can afford is $110.